A) \[1-\frac{1}{e}\]
B) \[2\,\left( 1-\frac{1}{e} \right)\]
C) \[{{e}^{-1}}-1\]
D) None of these
Correct Answer: B
Solution :
\[\int_{1/e}^{e}{|\log x|dx=\int_{1/e}^{1}{-\log x\,dx+\int_{1}^{e}{\,\log x\,dx}}}\] \[=[x-x\log x]_{1/e}^{1}+[x\log x-x]_{1}^{e}\] \[=(1-0)-\left\{ \frac{1}{e}-\frac{1}{e}(-1) \right\}+e-e+1\]\[=2-\frac{2}{e}=2\left( 1-\frac{1}{e} \right)\].
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